NEW YORK - CVS Caremark Corp. and Rite Aid Corp., two of the largest U.S. drugstore chains, said they are running short of influenza vaccines as an earlier and more severe flu season drives up demand from Michigan to New Jersey.

Requests for the shots at CVS are unprecedented for this time of year and the company is working to resupply its pharmacies and clinics, said Mike DeAngelis, a spokesman for the Woonsocket-based chain, in an e-mail. Rite Aid is moving supply from location to location, said Ashley Flower, a spokeswoman for the Camp Hill, Pennsylvania-based company.

This year’s flu season started earlier than in past years with 47 states now experiencing widespread flu, and New York state and Boston declaring health emergencies. That has sent more people than usual to pharmacies and doctors’ offices in search of the vaccine. While the Food and Drug Administration confirmed reports of spot shortages of vaccines, government officials said there isn’t a widespread lack of supply.

“If you seek it out, you should be able to find it,” Curtis Allen, a spokesman for the Atlanta-based Centers for Disease Control and Prevention, said yesterday in a telephone interview. “There has been a lot of attention to the severity of the season and therefore people are seeking out the vaccine.”

GlaxoSmithKline Plc, which makes a flu vaccine for the U.S. market, said that while some places might have low supply, it wasn’t aware of any national shortage.

“It appears there’s enough flu vaccine out there, it’s just a matter of where it is,” Rob Perry, a spokesman for the drugmaker, said yesterday in a telephone interview. The London- based company said it’s shipping the last of its stock from its Marietta, Pennsylvania, facility.

300,000 doses

AstraZeneca Plc’s MedImmune unit said it filled all current orders from customers and has a backup supply at the ready. The Gaithersburg, Maryland-based unit makes FluMist, a vaccine administered through nasal inhalation. It sold $161 million of the product in 2011, according to data compiled by Bloomberg.

“We currently have more than 300,000 extra doses that could be shipped,” Tor Constantino, a MedImmune spokesman, said in a telephone interview. The company hasn’t received requests for its additional supply, he said.

In addition, MedImmune has 250,000 flu vaccine doses on hold for the U.S. Defense Department and the children’s health program within Medicaid, the joint federal-state health plan for the poor. Those doses could be sold as well if the government doesn’t need them, Constantino said.

Glaxo’s Perry said his company doesn’t have additional supplies to distribute and hasn’t been contacted about producing more.

Vaccine makers produced 135 million doses of the immunization this year and had distributed 128.1 million as of Jan. 4, the CDC reported last week. At least 112 million people, 35 percent to 40 percent of those eligible, have gotten a flu shot this season, Michael Jhung, a CDC medical officer in the influenza division said last week.

Get the most up-to-date data on the Rhode Island and southern Massachusetts business community from the PBN List Center. Download and purchase PBN Lists as well as the complete Book of Lists in Excel format.